Continuous Boundary Conditions Research Articles

Analytical solution for one-dimensional nonlinear consolidation of double-layered soil with improved continuous drainage boundary

Following the assumptions proposed by Davis and Raymond, an analytical solution for one-dimensional nonlinear consolidation of double-layered soil under constant loading is derived by introducing an improved continuous drainage boundary condition. The effectiveness of the present solution is assessed by comparing against other existing analytical solutions and laboratory consolidation test results. A parametric study is then conducted to investigate the consolidation behaviour of double-layered soil for different interface parameters or stress ratios (i.e. final effective pressure over initial effective pressure, Nσ ). The results show that, the average consolidation degree defined by soil settlement U s increases with the increase of N σ, and the average consolidation degree defined by excess pore water pressure U p decreases with the increase of Nσ . The magnitude of U s is always larger than U p, and the difference between U s and U p increases with the increase of Nσ . Compared with the Xie's solution, the stress ratio Nσ has little effect on U p in the solution with continuous drainage boundary condition.

Fully-coupled electro-magneto-elastic behavior of unidirectional multiphased composites via finite-volume homogenization

The effective and localized electro-magneto-elastic behavior of periodic unidirectional composites is investigated in this work. Instead of adopting the classical micromechanics models or variational principle-based finite-element (FE) techniques, the finite-volume direct averaging micromechanics (FVDAM) is extended to fulfill this task by incorporating fully-coupled electro-magneto-elastic constitutive relations. Consistent with the mathematical homogenization theories, the mechanical displacements and electric/magnetic potentials are partitioned using two-scale expansion involving the macroscopic and fluctuating contributions. The generalized local stiffness matrices are constructed explicitly by relating the surface-averaged tractions, electric displacements, and magnetic inductions to the surface-averaged mechanical displacements and electric/magnetic potentials, followed which the continuity and periodic boundary conditions are applied. The homogenized coefficients and localized stress, electric/magnetic field distributions are validated extensively against the exact generalized Eshelby solution and an in-house FE program, as well as the experimental measurements, where perfect agreements are observed for all cases. The efficiency and convergence of the proposed multiphysics FVDAM (MFVDAM) are tested by comparing the execution time and localized fields as a function of mesh discretization, with the multiphysics FE (MFEM) results as references. Besides, the MFVDAM is encapsulated into the particle swarm optimization algorithm to deduce the optimal fiber volume fraction at which maximum magnetoelectric coupling effect may occur in the composite system with piezomagnetic ceramics reinforced with piezoelectric unidirectional fibers.

Solution of the Problem of Diffraction by a Plane Screen in a Plane Layered Medium with the Help of the Method of Continued Boundary Conditions

The 3D problem of diffraction of the field of a point source by a plane screen located on the interface of a plane layered medium is considered. The algorithm of the numerical solution of this problem is developed on the basis of the method of continued boundary conditions. In particular, the case, when the screen is located on the interface between two media and on the upper boundary of a dielectric layer surrounded by identical dielectric half-spaces, is considered. The correctness of the obtained results is controlled by verifying the accuracy of the fulfillment of the optical theorem. The angular dependences of the scattering pattern are constructed for the screens having circular, rectangular, and elliptic shapes.

Mathematical model of penetration of cylindrical electromagnetic fields with axial symmetry through the plane screen from permalloy

The method for solving the boundary-value problem of penetration of monochromatic electromagnetic fields with axial symmetry through the plane screen made from the permalloy is developed. The boundary-value problem is based on the use of differential Maxwell equations and complementary nonlinear differential equation for the field of magnetization, characterizing the permalloy. Classical boundary conditions of continuity of the tangential components of the fields and complementary boundary conditions for the field of magnetization on the face surfaces of the shield are used. For solution simplification of the boundary-value problem as a result of exclusion value the entering in nonlinear equation second-order infinitesimal, nonlinear task is transformed into linear task. Roots (wave numbers) of a dispersion algebraic equations of four order, which characterizing electromagnetic fields with axial symmetry in layer made from the permalloy, is constructed. The sequences of four forward and four backward counter-propagating electromagnetic waves with axial symmetry in the layer of permalloy is formed. Two-sided boundary conditions connecting electromagnetic fields with axial symmetry on both sides of the screen is constructed. The amplitudes of reflected and transient through the shield electromagnetic fields are calculated.

Scattering of SH Waves by a Partially Debonded Cylindrical Inclusion in the Covering Layer

This article presents analytical solutions to the problem of dynamic stress concentration and the surface displacement of a partially debonded cylindrical inclusion in the covering layer under the action of a steady-state horizontally polarized shear wave (SH wave); these solutions are using the complex function method and wave function expansion method. By applying the large-arc assumption method, the straight line boundary of the half-space covering layer is transformed into a curved boundary. The wave field of the debonded inclusion is constructed utilizing a Fourier series and boundary conditions of continuity. The impact of debonding upon the dynamic stress concentration and surface displacement around the cylindrical concrete or steel inclusion is analyzed through numerical examples of the SH waves that are incident at normal angles, from a harder medium to a softer medium and from a softer medium to a harder medium. The examples show that various factors (including the medium parameters of the soil layers and the inclusion, the frequency of the incident waves, and the debonding situations) jointly affect the dynamic stress concentration factor and the surface displacement around the structure.

Analysis of vibration characteristics of joined cylindrical-spherical shells

In this paper, the free and forced vibration of joined cylindrical-spherical shells (JCSSs) subjected to classical boundary conditions are investigated by a variational method. A JCSSs is divided into its components (i.e., cylindrical and spherical shells) at the cylinder-sphere junction. The interface continuity and geometric boundary conditions are approximately enforced by means of a modified variational principle and least-squares weighted residual method. Donnell shell theory is used to formulate the theoretical model. Double mixed series are adopted as admissible displacement functions for each shell component. In addition, the forced vibration response of the JCSSs is gained through the Newmark-β method. Through the comparison and analysis study, it is obvious that the proposed method has a good stable and rapid convergence property and the results of this paper closely agreed with those obtained by published literatures and the finite element method. The influence of structural parameters and different loading modes on free and forced vibration characteristics of JCSSs are considered.

Importance of Various Thermal Effects in Battery Modeling

Lithium-ion batteries exhibit highly temperature dependent performance and life cycle [1,2]. Safe operation of a battery is also closely related to its operating temperature [3]. Due to poor thermal transport within a Li-ion cell, specifically in the out of plane direction, temperature gradient and overheating can occur at moderate to high rates [4]. The poor thermal transport in the out of plane direction is because of the thermal resistance due to the multiple layers getting added up [5]. This leads to large total thermal resistance from the core of the cell to the surface. In addition to the layers, the interfaces between the layers also offer significant thermal interfacial resistance [6]. This makes it important to account for heat transfer within the cell in a battery model. From battery management system (BMS) standpoint, accounting for these thermal as well as electrochemical transport processes and reaction kinetics in a computationally efficient manner is critical. Various models have been proposed in the past for this purpose [7]. Among the various models, single particle model (SPM), pseudo two-dimensional (P2D) model, and pseudo three-dimensional (P3D) model are rigorously compared in their ability to predict performance of a battery under a wide variety of conditions. This includes high rates of charge and discharge, different cooling conditions at the cell surface, and a wide range of ambient/coolant temperatures. This study helps understand significance of accounting for various thermal effects in the context of accuracy of these different models. Results from this study give valuable insights into the capabilities of the different models.Additionally, using the P2D model, effect of thermal interfacial resistances at the cell stack level is studied in detail. Typically, thermal interfacial resistances are ignored in battery models which leads to temperature continuity at the interfaces [8]. However, based on the recent measurements, thermal interfacial resistance between the electrode and the separator has been found to be the rate limiting factor to heat transfer within a Li-ion cell [6]. This makes it important account for the interfacial heat transfer process by using appropriate thermal interfacial resistances between the layers, especially for a stack of cells. This has been achieved by altering the temperature continuity boundary condition at the interfaces in the P2D model. The key results from this study show that it is critical to account for this thermal effect for accurate predictions.

Analysis of the oblique incidence of periodic structures in a sound field by the finite-difference time-domain method

A method to analyze the acoustic characteristics of periodic structures is investigated. When a continuous boundary condition is introduced, the field in which a plane wave is normally incident on the periodic structure can be easily analyzed by the finite-difference time-domain (FDTD) method. However, when a plane wave source is obliquely incident, field mapping with auxiliary variables is necessary to remove the phase shift between unit cells. Here, a technique originally proposed for an electromagnetic field is applied to a sound field. The effects of the geometric parameters of the periodic structures on the sound pressure distribution and transmission loss in the mapped sound field are shown. This technique is validated by comparing the results with those in a field solved with the classical FDTD scheme. The dispersion relation and the stability condition for the time interval of the FDTD method for each incident angle of the plane wave in the mapped field are studied.

Numerical simulations and modelling of mass transfer through random assemblies of catalyst particles: From dilute to dense reactive particulate regime

We study mass transfer through random assemblies of fixed spherical catalyst particles experiencing an external convective-diffusive fluid stream. Chemical species are transported through the array and are diffused from fluid to solid phase through particles surface. An internal first order irreversible chemical reaction takes place within the porous catalyst particles. We address the determination of mass transfer coefficient by performing direct numerical simulations with fully internal-external coupling using concentration and flux continuity boundary conditions at the solid-fluid interface. We derive a theoretical prediction of the profiles of cup-mixing concentration, average of mean surface and average of mean volume concentration of the particles along the height of the domain. The model for the dimensionless mass transfer coefficient (‘reactive’ Sherwood number) is accounting for the five dimensionless parameters that control the physics of the system: the Reynolds number Re, the Schmidt number Sc, the Damköhler number Da, the internal-to-external diffusion coefficient ratio γ and the solid volume fraction αs. We use a coupled Sharp Interface/ Discrete Lagrange Multiplier-Fictitious Domain Method (SIM-DLM/FD), thoroughly validated in our previous study (Sulaiman et al., 2019) to test the accuracy of the model over a wide range of dimensionless parameters and solid volume faction (from dilute αs=0.1 to dense regime αs=0.5). We show and discuss the limitations of the proposed model.

Dynamic stability response of truncated nanocomposite conical shell with magnetostrictive face sheets utilizing higher order theory of sandwich panels

Present research is conducted in order to assess dynamic stability behavior of a nanocomposite sandwich truncated conical shells (NSTCS). In fact, graphene platelets (GPLs)-reinforced as core layer is encompassed through magnetostrictive layers as face sheets. For modeling the core layer and face sheets mathematically, higher order shear deformation theory (HSDT) besides first order shear deformation theory (FSDT) are utilized, respectively. To presume this sandwich structure much more realistic, Kelvin-Voigt model will be used. According to Hamilton's principle with respect to continuity boundary conditions, the governing equations are obtained. Utilizing differential cubature (DC) as well as Bolotin procedures, the governing equations will be solved and the region related to the dynamic instability is achieved. In this novel work, different variables covering various boundary edges, controller, cone's semi vertex angle, damping, feedback gain, proportion of core to face sheets thickness, dispersion kinds of GPLs and its volume percent will be studied. So as to indicate the accuracy of applied theories as well as methods, the results are collated with another paper. It is found that increment of GPLs volume percent leads to rise of excitation frequency.

Application of the Method of Continued Boundary Conditions to the Solution of the Problem of Wave Diffraction on Scatterers of Complex Geometry Located in Homogeneous and Heterogeneous Media

A method that allows modeling the scattering characteristics of bodies of arbitrary geometry has been proposed on the basis of the method of continued boundary conditions. The paper considers a two-dimensional problem of plane wave diffraction on dielectric bodies with complex cross-section geometry—in particular, on fractal-like bodies. Numerical algorithms for solving the diffraction problem based on systems of integral equations of the first and second kind have been compared. The method has been generalized to the problem of diffraction on a cylindrical body located in a homogeneous magnetodielectric half-space. The correctness of the method was confirmed by checking the fulfillment of the optical theorem for different bodies and by comparing with the results of calculations obtained by a modified method of discrete sources.

Dynamics of localized continuum inside a charged particle

This article explains how a charged body can retain its integrity despite electrostatic repulsion within itself. The study requires derivation of the field equations governing the velocity of any arbitrary element within the system. These relations are obtained from two Lagrangian principles based on obvious and least disruptive modifications of known concepts in classical mechanics. The two Lagrangians lead to a relativistic energy-momentum equation describing the motion and Maxwell’s equations quantifying the electromagnetic fields, respectively. The energy-momentum relation shows that rigid body motions creating stationary fields in a rotating frame is a viable solution for the velocity inside the continuum. It also yields a combined potential which remains constant throughout the rotating particle. This constancy coupled with Maxwell’s equations and boundary conditions for proper interfacial continuity provides the charge distribution and geometric shape required for continued coherence of the domain. The paper presents specific simulations for slender annuli steadily rotating about the axis of symmetry where the charge density and the axial width are plotted as radial functions. Curiously, when the analysis is extended to systems with different axes of rotation and symmetry, the proportionalities between energy and frequency as well as momentum and wave-number can be established. Such results are very similar to Planck’s and de Broglie’s laws, even though derived from classical principles. Thus, the presented theory might have deeper implications like, for example, in mathematical computation of fine structure constant.

Ritz Solution for Transient Analysis of Variable-Stiffness Shell Structures

The dynamic response of thin-walled structures is driven by mass and stiffness distribution. As such, variable-stiffness (VS) composites offer opportunities to tune structural dynamic responses. To this extent, efficient analysis tools become increasingly important for structural analysis and design purposes. In this work, an efficient and versatile Ritz method for free vibrations and linear transient analysis of VS doubly curved shell structures is presented. VS shell structures are modeled as an assembly of shell-like domains. The shell kinematics is based on the first-order shear deformation theory, and no further assumption is made on the shallowness or on the thinness of the structure. The description of the shell is provided by a rational Bézier surface representation, and general surface geometries can be represented. Legendre polynomials are employed to approximate the displacement field, and penalty techniques are used to enforce displacement continuity and kinematical boundary conditions. Classical Rayleigh damping is considered, and solutions are obtained through the Newmark integration. The resulting model allows a wide range of configurations and load cases for multicomponent, VS composite structures to be solved, providing the same levels of accuracy as finite element analysis, yet with a reduced number of variables and simpler data preparation.

A coupled contact model of cartilage lubrication in the mixed-mode regime under static compression

This study presents a coupled cartilage contact model, in which the contact gap and cartilage tissue are modelled as two poroelastic systems, linked by pressure and normal flux continuity boundary conditions. Using a tibial plug under indentation as a proof-of-concept model, the predictions support the weeping lubrication theory under static compression. Specifically, the interstitial fluid would exude from the underlying cartilage into the contact gap to extend the mixed-mode duration by > 20-fold compared to a no fluid exudation counterpart. Moreover, the traditional contact model, that does not consider the contact gap and cartilage fluid exchange, potentially overestimates the interstitial fluid pressure compared to the proposed coupled model. Parametric studies suggest that the increasing viscosity of synovial fluid prolongs the gap fluid pressurisation, while increasing the asperity stiffness reduces the gap fluid pressure but increases contact gap height.

Stability and dynamics of chiral nanoparticles in lateral optical binding induced by high-order Bessel beams

The generalized multi-particle Mie equation (GMM) and electromagnetic momentum (EM) theory are applied to investigate the stability and dynamics of chiral nanoparticles in lateral optical binding induced by a high-order Bessel beam (HOBB). Such non-diffracting light suppressed the influence of the axial intensity profile of the illuminating beams on the self-organization process which then depended critically upon the inter-particles interactions. The illuminating HOBB is described in terms of beam shape coefficients (BSCs) within the framework of generalized Lorenz–Mie theories (GLMT). Utilizing the addition theorem of the vector spherical wave functions (VSWFs), the interactive scattering coefficients are derived through the continuous boundary conditions on which the interaction of the chiral nanoparticles is considered. The observed lateral binding force (BF) dependence of the separation of optically bound particles on the incidence of HOBB is in agreement with earlier theoretical prediction when the chiral spheres degenerate into isotropic spheres. We discuss the influence of the different parameters of the incident Bessel beam and of the chiral body on lateral BF in detail. Linearly and circularly polarized incident Bessel beams are considered, and the corresponding lateral BFs are compared and analyzed. The polarizations of incident HOBB considerably influence the lateral BF of chiral nanoparticles. In binding chiral nanoparticles, the polarization of incident beams should be chosen in accordance with the chirality. This finding may provide a recipe to understand the light interaction with multiple chiral particles of arbitrary shapes with the aid of the analytical approach. It could be a promising avenue in controlling the optical micromanipulation on chiral structures self-arrangement.

Discrete Transparent Boundary Conditions for the Linearized Green--Naghdi System of Equations

In this paper, we introduce artificial boundary conditions for the linearized Green--Naghdi system of equations. The derivation of such continuous (respectively, discrete) boundary conditions inclu...

Upwind Biased Local RBF Scheme with PDE Centres for the Steady Convection Diffusion Equations with Continuous and Discontinuous Boundary Conditions

Upwind Biased Local RBF Scheme with PDE Centres for the Steady Convection Diffusion Equations with Continuous and Discontinuous Boundary Conditions

Study on the laminated frame strength of heavy-duty fracturing pump truck considering slip effect

A differential equation for the slip effect of a continuous superposition beam under asymmetric loads and flexible support was formulated in this study to study the effects of the stress distribution law and the slip effect of laminated frame under actual loads on the overall stress level of the frame. While considering continuity and free boundary conditions, a semi-analytical solution to the slippage of the superposed beam interface was proposed. An experiment for frame strength was designed based on the results of the numerical analysis. A field stress test was performed on the main frame and sub-frame, and the results demonstrated that slip effect could influence the overall mechanical properties of the laminated frame to some extent. Considering slip effect conforms to the actual mechanical properties of the laminated frame.

Применение метода продолженных граничных условий к решению задачи дифракции волн на рассеивателях сложной геометрии, расположенных в однородной и неоднородной средах

Based on the method of continued boundary conditions, a technique is proposed that allows modeling the scattering characteristics for bodies of arbitrary geometry. The two-dimensional problem of the diffraction of a plane wave by dielectric bodies with complex section geometry, in particular, by fractal-like bodies, is considered. Comparison of numerical algorithms for solving the diffraction problem based on systems of integral equations of the 1st and 2nd kind is carried out. The method is generalized to the problem of diffraction by a cylindrical body located in a homogeneous magnetodielectric half-space. The correctness of the method is confirmed by checking the fulfillment of the optical theorem for various bodies and by comparing it with the results of calculations obtained by the modified method of discrete sources.

Smoothness of Generalized Solutions of the Second and Third Boundary-Value Problems for Strongly Elliptic Differential-Difference Equations

In this paper, we investigate qualitative properties of solutions of boundary-value problems for strongly elliptic differential-difference equations. Earlier results establish the existence of generalized solutions of these problems. It was proved that smoothness of such solutions is preserved in some subdomains but can be violated on their boundaries even for infinitely smooth function on the right-hand side. For differential-difference equations on a segment with continuous right-hand sides and boundary conditions of the first, second, or the third kind, earlier we had obtained conditions on the coefficients of difference operators under which there is a classical solution of the problem that coincides with its generalized solution. Also, for the Dirichlet problem for strongly elliptic differential-difference equations, the necessary and sufficient conditions for smoothness of the generalized solution in Holder spaces on the boundaries between subdomains were obtained. The smoothness of solutions inside some subdomains except for ε-neighborhoods of angular points was established earlier as well. However, the problem of smoothness of generalized solutions of the second and the third boundary-value problems for strongly elliptic differential-difference equations remained uninvestigated. In this paper, we use approximation of the differential operator by finite-difference operators in order to increase the smoothness of generalized solutions of the second and the third boundary-value problems for strongly elliptic differential-difference equations in the scale of Sobolev spaces inside subdomains. We prove the corresponding theorem.